Tips and points to raise your horse's affecction:-) Brush the horse.-) Talk to the horse from the front.-) Leave it outside if it's sunny (and will be sunny tomorrow, too).-) Trot/ride every day, even for a short distance.-) Wish for it from the Goddess. (Not guaranteed)

Even if you check your status during the day to see if the horse has five hearts, you won't receive the trophy until the following day. This is also a requirement for one of the several endings for the game, the Horse Race with Bob.